Elliptic curve data - 100011.a1

Formats: - HTML - YAML - JSON - 2025-10-18T23:13:28.202163

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  abc_quality	double precision
  absD	numeric
  adelic_genus	integer
  adelic_index	integer
  adelic_level	bigint
  ainvs	numeric[]
  analytic_rank	smallint
  bad_primes	integer[]
  class_deg	smallint
  class_size	smallint
  cm	smallint
  conductor	integer
  degree	bigint
  elladic_images	text[]
  faltings_height	numeric
  faltings_index	smallint
  faltings_ratio	smallint
  iso_nlabel	smallint
  isogeny_degrees	smallint[]
  jinv	numeric[]
  lmfdb_iso	text
  lmfdb_label	text
  lmfdb_number	smallint
  manin_constant	smallint
  min_quad_twist_ainvs	numeric[]
  min_quad_twist_disc	smallint
  modell_images	text[]
  modm_images	text[]
  nonmax_primes	smallint[]
  nonmax_rad	integer
  num_bad_primes	smallint
  num_int_pts	integer
  optimality	smallint
  potential_good_reduction	boolean
  rank	smallint
  regulator	numeric
  semistable	boolean
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '100011e', 'Clabel': '100011e1', 'Cnumber': 1, 'abc_quality': 0.8462390254626199, 'absD': 99811078011, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 200022, 'ainvs': [0, 1, 1, 1070, 7408], 'analytic_rank': 1, 'bad_primes': [3, 17, 37, 53], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 100011, 'degree': 121968, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.79881472374661448562626039640', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1], 'jinv': [135353378115584, 99811078011], 'lmfdb_iso': '100011.a', 'lmfdb_label': '100011.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, 1070, 7408], 'min_quad_twist_disc': 1, 'modell_images': [], 'modm_images': ['200022.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 6, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.21548872029837036950740030460', 'prec': 103}, 'semistable': True, 'serre_invariants': [[3, 4, 901], [7, 2, 33337], [17, 18, 5883], [37, 38, 2703], [53, 54, 1887]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.79881472374661448562626039640', 'prec': 103}, 'szpiro_ratio': 2.826266817830107, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• ec_classdata •

  Column	Type
  anlist	smallint[]
  aplist	smallint[]
  class_deg	smallint
  class_size	smallint
  conductor	integer
  isogeny_matrix	smallint[]
  lmfdb_iso	text
  trace_hash	bigint

  
  {'anlist': [0, 1, -2, 1, 2, 1, -2, 0, 0, 1, -2, -5, 2, -4, 0, 1, -4, 1, -2, -4, 2], 'aplist': [-2, 1, 1, 0, -5, -4, 1, -4, 0, -6, -2, 1, 12, 4, -6, 1, -3, -8, 8, 2, 7, 6, -9, 7, 13], 'class_deg': 1, 'class_size': 1, 'conductor': 100011, 'isogeny_matrix': [[1]], 'lmfdb_iso': '100011.a', 'trace_hash': 1687195934113870876}
• ec_mwbsd •

  Column	Type
  area	numeric
  conductor	integer
  gens	numeric[]
  heights	numeric[]
  lmfdb_label	text
  ngens	smallint
  rank_bounds	smallint[]
  real_period	numeric
  sha_an	numeric
  special_value	numeric
  tamagawa_product	integer
  torsion_generators	numeric[]
  xcoord_integral_points	numeric[]

  
  {'area': {'__RealLiteral__': 0, 'data': '0.20237569202069633798828312401', 'prec': 103}, 'conductor': 100011, 'gens': [[-4, 55, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.21548872029837036950740030460', 'prec': 103}], 'lmfdb_label': '100011.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.67854448449059215881870130631', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0705923351962976231214469767687269617', 'prec': 130}, 'tamagawa_product': 21, 'torsion_generators': [], 'xcoord_integral_points': [-4, 17, 107]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 1, 0], '3': [6, 0], '5': [1, 0], '7': [1, 1, 0], '11': [3, 0], '13': [1, 0], '17': [2, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [2, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0], '53': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '100011.a1'}
• ec_torsion_growth •

  Column	Type
  degree	smallint
  field	numeric[]
  lmfdb_label	text
  torsion	smallint[]

  
  
  • id: 4641112
    {'degree': 3, 'field': [-342, 48, 0, 1], 'lmfdb_label': '100011.a1', 'torsion': [2]}
  • id: 4641113
    {'degree': 6, 'field': [3600396, 0, 20736, 0, 288, 0, 1], 'lmfdb_label': '100011.a1', 'torsion': [2, 2]}
  • id: 4641114
    {'degree': 8, 'field': [-351, 81, -144, 125, -59, -7, 7, -4, 1], 'lmfdb_label': '100011.a1', 'torsion': [3]}
  • id: 4641115
    {'degree': 12, 'field': [325255465361, 199004537148, 6392029646, -681602308, 848555991, 152581168, 708120, 489600, 98227, 6700, -78, -4, 1], 'lmfdb_label': '100011.a1', 'torsion': [4]}
• ec_localdata •

  Column	Type
  conductor	integer
  conductor_valuation	smallint
  discriminant_valuation	smallint
  j_denominator_valuation	smallint
  kodaira_symbol	smallint
  lmfdb_label	text
  prime	integer
  reduction_type	smallint
  root_number	smallint
  tamagawa_number	smallint

  
  
  • id: 2453855
    {'conductor': 100011, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '100011.a1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
  • id: 2453856
    {'conductor': 100011, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '100011.a1', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 2453857
    {'conductor': 100011, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '100011.a1', 'prime': 37, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 2453858
    {'conductor': 100011, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '100011.a1', 'prime': 53, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  {'adelic_gens': [[151369, 2, 151369, 3], [109447, 2, 109447, 3], [200021, 2, 200020, 3], [1, 0, 2, 1], [1, 2, 0, 1], [133349, 2, 133349, 3], [11767, 2, 11767, 3], [1, 1, 200021, 0]], 'adelic_image': '200022.2.0.?', 'conductor': 100011, 'lmfdb_label': '100011.a1', 'prime': 0}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 5202084
    {'lmfdb_iso': '100011.a', 'p': 5, 'prec': 20, 'unit': 76334315704003, 'val': -1}
  • id: 5202083
    {'lmfdb_iso': '100011.a', 'p': 11, 'prec': 20, 'unit': 275225914718201569, 'val': 3}
  • id: 5202089
    {'lmfdb_iso': '100011.a', 'p': 13, 'prec': 20, 'unit': 876984616256271216517, 'val': 1}
  • id: 5202092
    {'lmfdb_iso': '100011.a', 'p': 19, 'prec': 20, 'unit': 1748241699753310448054846, 'val': 1}
  • id: 5202088
    {'lmfdb_iso': '100011.a', 'p': 29, 'prec': 20, 'unit': 993270775403579758403715135, 'val': 1}
  • id: 5202098
    {'lmfdb_iso': '100011.a', 'p': 31, 'prec': 20, 'unit': 10750854715077235054248265293, 'val': 1}
  • id: 5202086
    {'lmfdb_iso': '100011.a', 'p': 41, 'prec': 20, 'unit': 2110414365836565334134709473337, 'val': 1}
  • id: 5202087
    {'lmfdb_iso': '100011.a', 'p': 43, 'prec': 20, 'unit': 4942270340088243260345267838471, 'val': 1}
  • id: 5202096
    {'lmfdb_iso': '100011.a', 'p': 47, 'prec': 20, 'unit': 47594462520587237276261151854319, 'val': 1}
  • id: 5202091
    {'lmfdb_iso': '100011.a', 'p': 59, 'prec': 20, 'unit': 3247675906041646901212046716414624, 'val': 1}
  • id: 5202097
    {'lmfdb_iso': '100011.a', 'p': 61, 'prec': 20, 'unit': 1450967115701109691379760929433250, 'val': 1}
  • id: 5202082
    {'lmfdb_iso': '100011.a', 'p': 67, 'prec': 20, 'unit': 49335683867923055476117987387810339, 'val': 1}
  • id: 5202085
    {'lmfdb_iso': '100011.a', 'p': 71, 'prec': 20, 'unit': 8109768744114716438291967000408257, 'val': 1}
  • id: 5202093
    {'lmfdb_iso': '100011.a', 'p': 73, 'prec': 20, 'unit': 155992937118080707976670345548809039, 'val': 1}
  • id: 5202090
    {'lmfdb_iso': '100011.a', 'p': 79, 'prec': 20, 'unit': 37729996339305274045719484239932326, 'val': 1}
  • id: 5202094
    {'lmfdb_iso': '100011.a', 'p': 83, 'prec': 20, 'unit': 1456803336696205809354475418723374525, 'val': 1}
  • id: 5202095
    {'lmfdb_iso': '100011.a', 'p': 89, 'prec': 20, 'unit': 2690988898428472053743335404408547389, 'val': 1}
  • id: 5202081
    {'lmfdb_iso': '100011.a', 'p': 97, 'prec': 20, 'unit': 6865482835851379999539869708456069515, 'val': 1}